I've followed the case somewhat. It took some time to build the case. The murders happened around 4am, so there where no eyeballs outside of the actual crime scene. There were just some fuzzy videos of a white car passing by a gas station and a location near the murders. It took the FBI forensics team time to narrow down the make of the car and the year it was made. One of the key determining factors is the car didn't have front license plates. The word went out and an alert Washington State University police officer found a car possibly matching the description. The police were then able to build their case against the accused murderer.
At some point, the police announced what exact car was being sought. At that point, all Kohberger’s family members had the opportunity to report the car, and none did.